Apartment Acoustics Analyzed using the Acoustic Diffusion Equation
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The steady state sound pressure level distribution from a TV in a two-room apartment is computed
The simulation uses the Acoustic Diffusion Equation interface
An approximate expression for the direct sound is added in the living room
Geometry and Mesh
The geometry consists of a living room, a bedroom, and some
The acoustic diffusion equation does not have any strong demands on the mesh
The simulation is driven by an energy flux assigned to the speaker fronts
Both rooms have their diffusion coefficient calculated using the cubic room mean free path model:
Between the rooms, a room coupling condition applies a 10 dB transmission loss (TL) representing a door
c = speed of sound
V = room volume
S = area of walls, floor, ceiling
The simulation is solved for a flat band, i.e. with absorption coefficients considered independent of the frequency
An absorption coefficient of 0.7 is applied to the soft surfaces and an absorption coefficient of 0.25 to the hard surfaces. Especially the latter is a little higher than typical, to compensate for the lack of carpets, curtains, etc.
For more realistic results, it is recommended that you modify the application to include different absorption coefficients for different materials and in different frequency bands
The acoustic diffusion equation does not include direct sound
Assuming that the speakers send out sound isotropically in a half-space, most of the living room is expected to experience a direct sound intensity from each speaker approximated by the expression corresponding to a squared pressure amplitude
The total sound pressure level then becomes
in the living room
in the bedroom
Pn = Power from speaker n
rn = distance to center of speaker n
Z0 = characteristic air impedance
pd = diffuse pressure
pref = 20⋅10-6 Pa
See also reference: A. Billon, J. Picaut, V. Valeau, and A. Sakout, “Acoustic Predictions in Industrial Spaces Using a Diffusion Model”, Advances in Acoustics and Vibration, Volume 2012 (2012).
23 dB drop between the red dots (listening and sleeping positions)
Sound pressure level (dB)
The Schroeder frequencies for the bedroom and living room evaluate to 183 Hz and 167 Hz respectively. The acoustic diffusion equation is a better approximation the higher the frequency, and should not be used below the Schroeder frequency.
Adding the direct sound has increased the sound pressure level in the listening position above the couch by 1.8 dB.